Question

Consider the following macroeconomy. All amounts are in millions (m.) of $; T=net taxes, which are fixed:

C = 750 + .8 Y_D

                                                            I = 1200

                                                            G = 250

                                                            T = 150

                a. This country’s Parliament passes legislation to have a balanced-budget amendment. What will be the value

             of this country’s balanced-budget multiplier (BBM)? Explain. Calculate the changes in the following variables if

             this country’s Parliament increases its G to $550 m: the GBD (govt budget deficit); eqm Y; and (net) taxes, T?    

             Show what this G increase does to the Z-Y space graph.

                b. What is meant by the “Paradox of Thrift” (POT), aka the Paradox of Saving? Why is it a paradox? Go back to the original eqm of part a. Now prove using multiplier analysis that the POT holds in this economy if c_o falls by $200 m. (ceteris paribus, cet. par.) by either calculating S private (S^p) at the initial eqm Y and then calculate S^p again after the attempt to increase S^p OR prove that the POT occurs using the appropriate math. Show what     happens (cet. par.) using the Z-Y space graph.

Answer 1

A) government spending multiplier=1/(1-mpc)

Tax multiplier=-mpc/(1-mpc)

Balance budget Multiplier=government spending Multiplier+ tax multiplier=1/(1-mpc)-mpc/(1-mpc)=(1-mpc)/(1-mpc)=1

So balance budget Multiplier is Equal to 1.

Government spending Multiplier=1/(1-mpc)=1/(1-0.8)=1/0.2=5

∆Y=∆G* government spending multiplier

∆G=550-250=300

∆ Y=300*5=1500

So output will increase by 1500.

Budget deficit ( initially)=250-150=100

Budget deficit( after change in G)=government spending- tax=550-150=400

∆ budget deficit=400-100=300

Net taxes=taxes - G

Net taxes( initially)=150-250=-100

Net taxes( after change in G)=150-550=-400

∆ in net taxes=-400-(-100)=-400+100=-300

B)paradox of thrift states when people try to save more ,it leads to less saving or same savings but on other side it leads to output decline.

It is paradox because people try to increase their saving but that results into fall in their saving.

Y=750+0.8(y-150)+1200+250=2080+0.8y

Y=2080/0.2=10.400

Saving=-750+0.2*(10,400-150)=-750+0.2*(10,250)=1300

Fall in Co ,means decrease in autonomous consumption (or Increase in autonomous saving) by 200.

New C=550+0.8Yd

∆ Y=∆Co*autonomous spending Multiplier=-200*5=-1000

New Y=10,400-1000=9400

New saving=-550+0.2*(9400-150)=-550+0.2*9250=1300

So as you can see saving is remain unchanged when autonomous saving Increase but output decline by 1000.